This ball design is inspired by the sphericon class of solids.
If we are given a regular polygon with n > 2 vertexes, we can create several sphericons from it:
Choose one of the polygons symmetry axis and let it rotate around this axis. Cut the resulting rotation solid into two halves, rotate one half by k * 360°/n for a k = 1,2,...,n-1, then glue together the two parts again. The result is the sphericon (n,k) - or its dual one, which exists if n is an even number.
This model was made using OpenSCAD. A hollow sphericon was blown up a bit which turned its edges into broad gaps between the faces.
There are some more similar models available.